CLEP College Mathematics

CLEP College

Mathematics

AT A GLANCE

Description of the Examination

CLEP?

The

College Mathematics examination covers

material generally taught in a college course for

nonmathematics majors and majors in fields not requiring

knowledge of advanced mathematics.

The exam contains 60 questions to be answered in

97 minutes. Some of these are pretest questions that won't

be scored. Any time candidates spend on tutorials and

providing personal information is in addition to the actual

testing time.

An online scientific (nongraphing) calculator will be available

during the exam. Although a calculator isn't necessary

to answer most of the questions, the solutions of a few

problems may be difficult to obtain without a calculator.

Because no calculator is allowed during the exam except for

the online calculator provided, it's recommended that prior

to the exam, you become familiar with the use of the online

calculator.

For more information about downloading the practice

version of the scientific (nongraphing) calculator, please visit

the College Mathematics description on the CLEP website:

clep.science-and-mathematics/

college-mathematics.

It's assumed that candidates are familiar with currently

taught mathematics vocabulary, symbols, and notation.

Knowledge and Skills Required

Questions on the College Mathematics exam require

candidates to demonstrate the following abilities in the

approximate proportions indicated.

¡ì Solving routine, straightforward problems (about 50%

of the exam)

¡ì Solving nonroutine problems requiring an

understanding of concepts and the application of skills

and concepts (about 50% of the exam)

The subject matter of the College Mathematics exam is

drawn from the following topics. The percentages next to

the main topics indicate the approximate percentage of

exam questions on each topic.

20% ALGEBRA AND FUNCTIONS

¡ì Solving equations, linear inequalities, and systems of

linear equations by analytic and graphical methods

¡ì Properties of triangles and quadrilaterals: perimeter,

area, similarity, and the Pythagorean theorem

¡ì Interpretation, representation, and evaluation of

functions: numerical, graphical, symbolic, and

descriptive methods

¡ì Parallel and perpendicular lines

¡ì Graphs of functions: translations, horizontal and vertical

reflections, and symmetry about the x-axis, the y-axis,

and the origin

¡ì Linear and exponential growth

¡ì Applications

¡ì Types of functions that will be considered are linear,

polynomial, radical, exponential, logarithmic, and

piecewise defined.

10% COUNTING AND PROBABILITY

¡ì Properties of circles: circumference, area, central

angles, inscribed angles, and sectors

¡ì Applications

15% LOGIC AND SETS

¡ì Logical operations and statements: conditional

statements, conjunctions, disjunctions, negations,

hypotheses, logical conclusions, converses, inverses,

counterexamples, contrapositives, and logical

equivalence

¡ì Set relationships, subsets, disjoint sets, equality of sets,

and Venn diagrams

¡ì Counting problems: the multiplication rule,

combinations, and permutations

¡ì Operations on sets: union, intersection, complement,

and Cartesian product

¡ì Probability: union, intersection, independent events,

mutually exclusive events, complementary events,

conditional probabilities, and expected value

¡ì Applications

¡ì Applications

15% DATA ANALYSIS AND STATISTICS

10% NUMBERS

¡ì Properties of numbers and their operations: integers

and rational, irrational, and real numbers (including

recognizing rational and irrational numbers)

¡ì Data interpretation and representation: tables,

bar graphs, line graphs, circle graphs, pie charts,

scatterplots, and histograms

¡ì Elementary number theory: factors and divisibility,

primes and composites, odd and even integers, and the

fundamental theorem of arithmetic

¡ì Numerical summaries of data: mean (average), median,

mode, and range

¡ì Measurement: unit conversion, scientific notation, and

numerical precision

¡ì Standard deviation and normal distribution (conceptual

questions only)

¡ì Absolute value

¡ì Applications

20% FINANCIAL MATHEMATICS

¡ì Percents, percent change, markups, discounts, taxes,

profit, and loss

¡ì Interest: simple, compound, continuous interest,

effective interest rate, and effective annual yield or

annual percentage rate (APR)

¡ì Present value and future value

¡ì Applications

2

10% GEOMETRY

¡ì Applications

Sample Test Questions

Study Resources

The following sample questions don't appear on an actual

CLEP exam. They're intended to give potential test takers

an indication of the format and difficulty level of the exam

and to provide content for practice and review. Knowing

the correct answers to all of the sample questions isn't a

guarantee of satisfactory performance on the exam.

Most textbooks used in college-level mathematics

courses cover the topics in the outline given earlier,

but the approaches to certain topics and the emphasis

given to them may differ. To prepare for the College

Mathematics exam, it's advisable to study one or more

introductory college-level mathematics textbooks,

which can be found in most college bookstores or

online. Elementary algebra textbooks also cover many

of the topics on the College Mathematics exam. When

selecting a textbook, check the table of contents against

the knowledge and skills required for the test. Visit

clep.earn-college-credit/practice for

additional math resources. You can also find suggestions for

exam preparation in Chapter IV of the CLEP Official Study

Guide. In addition, college faculty post their course materials

on their school¡¯s website.

Directions: An online scientific calculator will be available for

the questions in this test. Some questions will require you to

select from among four choices. For these questions, select

the BEST of the choices given. Some questions will require

you to type a numerical answer in the box provided. Some

questions will refer to a table in which statements appear

in the first column. For each statement, select the correct

properties by checking the appropriate cell(s) in the table.

Notes: (1) Unless otherwise specified, the domain of any

function f is assumed to be the set of all real

numbers x for which f (x) is a real number.

(2) Figures that accompany questions are intended

to provide information useful in answering the

questions. The figures are drawn as accurately

as possible EXCEPT when it's stated in a specific

question that the figure isn't drawn to scale.

Sample Questions

1.

(3) For a universal set U and X, a subset of U, the

complement of X, denoted as X C, is defined as

the set of elements of U that are not in X.

(4) Profit equals Revenue minus Cost.

(5) If a principal of P dollars is invested at an annual

interest rate r, compounded n times per year,

and no further withdrawals or deposits are made

to the account, then the future value A, the

account balance after t years, is given by

the formula A = P 1+

r

n

nt

(7) At an interest rate r, compounded n times

per year, the effective annual yield, or annual

percentage rate (APR), is given by the

formula APR = 1+

3

r

n

n

2

2.

1.

(4 ¡Á10?5 )

3

(2 ¡Á106 )

A.

B.

C.

D.

.

(6) If a principal of P dollars is invested at an annual

interest rate r and is compounded continuously,

and no further withdrawals or deposits are

made to the account, then the future value A,

the account balance after t years, is given by the

formula A = Pe rt.

Audrey deposited $10,000 into a 3-year certificate of

deposit that earned 10% annual interest, compounded

annually. Audrey made no additional deposits to or

withdrawals from the certificate of deposit. What was

the value of the certificate of deposit at the end of the

3-year period?

A. $13,000

B. $13,300

C. $13,310

D. $13,401

3.

=

2 x 10 ¨C2?

1.3 x 10 ¨C2

1.6 x 10 10

2 x 10 14

If P dollars is invested in a savings account that pays

5% annual interest, compounded continuously,

in how many years will the account value be equal to

2P dollars?

A. 20 ln(2) years

B. 5 ln(2) years

C. 10 years

D. 20 years

4.

Assume that a and b are positive integers. For each

statement below, determine whether the statement is true

or false, and indicate your answer in the appropriate box.

Statement

8.

6

11

B. 26

C. 38

D. 48

A.

True False

2

2

If a is divisible by b, then a is divisible by b .

2

If a is divisible by b, then a is divisible by b.

2

If a is divisible by b , then a is divisible by b.

5.

9.

From 1950 to 1990, the population of Country W

increased by 40%. From 1990 to 2012, the population of

Country W increased by 10%. What is the percent increase

in the population of Country W from 1950 to 2012?

%

6.

Let P(E) represent the probability of event E. Let A and B

be events with P(B) = 0.7, and P(A¡ÉB) = 0.2. What is the

value of P(A¡ÈB)?

A. 1.0

B. 0.9

C. 0.8

D. 0.7

Number of Teachers

600

500

400

300

200

100

40

A

500

2005

2010

375 400

300

0

7.

NUMBER OF TEACHERS IN FOUR CITIES,

2005 AND 2010

B

City

C

D

The chart above shows the number of teachers in City A,

City B, City C, and City D in 2005 and 2010. Which

city had the greatest percent increase in the number of

teachers from 2005 to 2010 ?

A. City A

B. City B

C. City C

D. City D

x ?2

, then f ( g (¨C4)) =

x +3

There are 220 seniors at a certain school. Among all

seniors at the school, 45 took calculus, 55 took physics,

and 10 took both. How many seniors took neither

calculus nor physics?

A. 90

B. 100

C. 120

D. 130

Airline/ Departure

Morning

Afternoon

Total

Airmoon flights

4

6

10

Airsun flights

7

8

15

Total

11

14

25

10. There are 10 Airmoon flights and 15 Airsun flights daily

from Yorktown to Newcity, as shown in the table above.

The table shows that 4 Airmoon and 7 Airsun flights

depart in the morning and the remaining flights depart

in the afternoon. If a flight is to be selected at random

from among the flights that depart in the afternoon

from Yorktown to Newcity, what is the probability that

the flight selected will be an Airmoon flight?

A.

100 115

100

If f (x) = x2 + x ¨C 4 and g(x) =

B.

C.

D.

6

25

6

14

10

25

14

25

11. In a sleep study, there are 50 people who are 20 years old,

50 people who are 25 years old, and 50 people who

are 30 years old. If an additional 20-year-old person

participates in the study, what happens to the average age,

the median age, and the age range of the participants in

the study?

Increases Decreases Does Not Change

Average age

Median age

Age range

Click on your choices.

4

Credit Recommendations

The American Council on Education has recommended

that colleges grant three credits for a score of 50, which is

equivalent to a course grade of C, on the CLEP College

Mathematics exam. Each college, however, is responsible

for setting its own policy. For candidates with satisfactory

scores on the College Mathematics exam, colleges may

grant credit toward fulfillment of a distribution requirement,

or for a particular course that matches the exam in content.

Check with your school to find out the score it requires for

granting credit, the number of credit hours granted, and the

course that can be bypassed with a passing score.

Answers to Sample Questions:

1-C; 2-A; 3-A; 4-see below; 5-54; 6-C; 7-B; 8-C; 9-D; 10-B;

11-see below

4.

Statement

True False

2

2

If a is divisible by b, then a is divisible by b .

?

2

?

If a is divisible by b, then a is divisible by b.

2

If a is divisible by b , then a is divisible by b.

?

11.

Increases

Average age

5

Decreases Does Not Change

?

Median age

?

Age range

?

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